The invention of the transformer architecture has revolutionized Artificial Intelligence (AI), yielding unprecedented success in areas such as natural language processing, computer vision, and multimodal reasoning. Despite these advances, it is unclear whether transformers are able to learn and implement precise algorithms. Here, we demonstrate that transformers can exactly implement a fundamental and widely used algorithm for $k$-means clustering: Lloyd's algorithm. First, we theoretically prove the existence of such a transformer architecture, which we term the $k$-means transformer, that exactly implements Lloyd's algorithm for $k$-means clustering using the standard ingredients of modern transformers: attention and residual connections. Next, we numerically implement this transformer and demonstrate in experiments the exact correspondence between our architecture and Lloyd's algorithm, providing a fully neural implementation of $k$-means clustering. Finally, we demonstrate that interpretable alterations (e.g., incorporating layer normalizations or multilayer perceptrons) to this architecture yields diverse and novel variants of clustering algorithms, such as soft $k$-means, spherical $k$-means, trimmed $k$-means, and more. Collectively, our findings demonstrate how transformer mechanisms can precisely map onto algorithmic procedures, offering a clear and interpretable perspective on implementing precise algorithms in transformers.

We present an application of a foundation model for small- to medium-sized tabular data (TabPFN), to sub-national yield forecasting task in South Africa. TabPFN has recently demonstrated superior performance compared to traditional machine learning (ML) models in various regression and classification tasks. We used the dekadal (10-days) time series of Earth Observation (EO; FAPAR and soil moisture) and gridded weather data (air temperature, precipitation and radiation) to forecast the yield of summer crops at the sub-national level. The crop yield data was available for 23 years and for up to 8 provinces. Covariate variables for TabPFN (i.e., EO and weather) were extracted by region and aggregated at a monthly scale. We benchmarked the results of the TabPFN against six ML models and three baseline models. Leave-one-year-out cross-validation experiment setting was used in order to ensure the assessment of the models capacity to forecast an unseen year. Results showed that TabPFN and ML models exhibit comparable accuracy, outperforming the baselines. Nonetheless, TabPFN demonstrated superior practical utility due to its significantly faster tuning time and reduced requirement for feature engineering. This renders TabPFN a more viable option for real-world operation yield forecasting applications, where efficiency and ease of implementation are paramount.

Interpretability plays a vital role in aligning and deploying deep learning models in critical care, especially in constantly evolving conditions that influence patient survival. However, common interpretability algorithms face unique challenges when applied to dynamic prediction tasks, where patient trajectories evolve over time. Gradient, Occlusion, and Permutation-based methods often struggle with time-varying target dependency and temporal smoothness. This work systematically analyzes these failure modes and supports learnable mask-based interpretability frameworks as alternatives, which can incorporate temporal continuity and label consistency constraints to learn feature importance over time. Here, we propose that learnable mask-based approaches for dynamic timeseries prediction problems provide more reliable and consistent interpretations for applications in critical care and similar domains.

Traditional models of accent perception underestimate the role of gradient variations in phonological features which listeners rely upon for their accent judgments. We investigate how pretrained representations from current self-supervised learning (SSL) models of speech encode phonological feature-level variations that influence the perception of segmental accent. We focus on three segments: the labiodental approximant, the rhotic tap, and the retroflex stop, which are uniformly produced in the English of native speakers of Hindi as well as other languages in the Indian sub-continent. We use the CSLU Foreign Accented English corpus (Lander, 2007) to extract, for these segments, phonological feature probabilities using Phonet (Vásquez-Correa et al., 2019) and pretrained representations from Wav2Vec2-BERT (Barrault et al., 2023) and WavLM (Chen et al., 2022) along with accent judgements by native speakers of American English. Probing analyses show that accent strength is best predicted by a subset of the segment's pretrained representation features, in which perceptually salient phonological features that contrast the expected American English and realized non-native English segments are given prominent weighting. A multinomial logistic regression of pretrained representation-based segment distances from American and Indian English baselines on accent ratings reveals strong associations between the odds of accent strength and distances from the baselines, in the expected directions. These results highlight the value of self-supervised speech representations for modeling accent perception using interpretable phonological features.

Cone-beam computed tomography (CBCT) using only a few X-ray projection views enables faster scans with lower radiation dose, but the resulting severe under-sampling causes strong artifacts and poor spatial coverage. We address these challenges in a unified framework. First, we replace conventional UNet/ResNet encoders with TransUNet, a hybrid CNN-Transformer model. Convolutional layers capture local details, while self-attention layers enhance global context. We adapt TransUNet to CBCT by combining multi-scale features, querying view-specific features per 3D point, and adding a lightweight attenuation-prediction head. This yields Trans-CBCT, which surpasses prior baselines by 1.17 dB PSNR and 0.0163 SSIM on the LUNA16 dataset with six views. Second, we introduce a neighbor-aware Point Transformer to enforce volumetric coherence. This module uses 3D positional encoding and attention over k-nearest neighbors to improve spatial consistency. The resulting model, Trans$^2$-CBCT, provides an additional gain of 0.63 dB PSNR and 0.0117 SSIM. Experiments on LUNA16 and ToothFairy show consistent gains from six to ten views, validating the effectiveness of combining CNN-Transformer features with point-based geometry reasoning for sparse-view CBCT reconstruction.

Traditional instrumental variable (IV) estimators face a fundamental constraint: they can only accommodate as many endogenous treatment variables as available instruments. This limitation becomes particularly challenging in settings where the treatment is presented in a high-dimensional and unstructured manner (e.g. descriptions of patient treatment pathways in a hospital). In such settings, researchers typically resort to applying unsupervised dimension reduction techniques to learn a low-dimensional treatment representation prior to implementing IV regression analysis. We show that such methods can suffer from substantial omitted variable bias due to implicit regularization in the representation learning step. We propose a novel approach to construct treatment representations by explicitly incorporating instrumental variables during the representation learning process. Our approach provides a framework for handling high-dimensional endogenous variables with limited instruments. We demonstrate both theoretically and empirically that fitting IV models on these instrument-informed representations ensures identification of directions that optimize outcome prediction. Our experiments show that our proposed methodology improves upon the conventional two-stage approaches that perform dimension reduction without incorporating instrument information.

3D point cloud semantic segmentation (PCSS) is a cornerstone for environmental perception in robotic systems and autonomous driving, enabling precise scene understanding through point-wise classification. While unsupervised domain adaptation (UDA) mitigates label scarcity in PCSS, existing methods critically overlook the inherent vulnerability to real-world perturbations (e.g., snow, fog, rain) and adversarial distortions. This work first identifies two intrinsic limitations that undermine current PCSS-UDA robustness: (a) unsupervised features overlap from unaligned boundaries in shared-class regions and (b) feature structure erosion caused by domain-invariant learning that suppresses target-specific patterns. To address the proposed problems, we propose a tripartite framework consisting of: 1) a robustness evaluation model quantifying resilience against adversarial attack/corruption types through robustness metrics; 2) an invertible attention alignment module (IAAM) enabling bidirectional domain mapping while preserving discriminative structure via attention-guided overlap suppression; and 3) a contrastive memory bank with quality-aware contrastive learning that progressively refines pseudo-labels with feature quality for more discriminative representations. Extensive experiments on SynLiDAR-to-SemanticPOSS adaptation demonstrate a maximum mIoU improvement of 14.3\% under adversarial attack.

Locally adapting parameters within Markov chain Monte Carlo methods while preserving reversibility is notoriously difficult. The success of the No-U-Turn Sampler (NUTS) largely stems from its clever local adaptation of the integration time in Hamiltonian Monte Carlo via a geometric U-turn condition. However, posterior distributions frequently exhibit multi-scale geometries with extreme variations in scale, making it necessary to also adapt the leapfrog integrator's step size locally and dynamically. Despite its practical importance, this problem has remained largely open since the introduction of NUTS by Hoffman and Gelman (2014). To address this issue, we introduce the Within-orbit Adaptive Leapfrog No-U-Turn Sampler (WALNUTS), a generalization of NUTS that adapts the leapfrog step size at fixed intervals of simulated time as the orbit evolves. At each interval, the algorithm selects the largest step size from a dyadic schedule that keeps the energy error below a user-specified threshold. Like NUTS, WALNUTS employs biased progressive state selection to favor states with positions that are further from the initial point along the orbit. Empirical evaluations on multiscale target distributions, including Neal's funnel and the Stock-Watson stochastic volatility time-series model, demonstrate that WALNUTS achieves substantial improvements in sampling efficiency and robustness compared to standard NUTS.

In this study, we apply machine learning and software engineering in analyzing air pollution levels in City of Baltimore. The data model was fed with three primary data sources: 1) a biased method of estimating insurance risk used by homeowners loan corporation, 2) demographics of Baltimore residents, and 3) census data estimate of NO2 and PM2.5 concentrations. The dataset covers 650,643 Baltimore residents in 44.7 million residents in 202 major cities in US. The results show that air pollution levels have a clear association with the biased insurance estimating method. Great disparities present in NO2 level between more desirable and low income blocks. Similar disparities exist in air pollution level between residents' ethnicity. As Baltimore population consists of a greater proportion of people of color, the finding reveals how decades old policies has continued to discriminate and affect quality of life of Baltimore citizens today.

Vector representations of contextual embeddings learned by pre-trained large language models (LLMs) are effective in various downstream tasks in numerical domains such as time series forecasting. Despite their significant benefits, the tendency of LLMs to hallucinate in such domains can have severe consequences in applications such as energy, nature, finance, healthcare, retail and transportation, among others. To guarantee prediction reliability and accuracy in numerical domains, it is necessary to open the black box behind the LLM and provide performance guarantees through explanation. However, there is little theoretical understanding of when pre-trained language models help solve numerical downstream tasks. This paper seeks to bridge this gap by understanding when the next-word prediction capability of LLMs can be adapted to numerical domains through a novel analysis based on the concept of isotropy in the contextual embedding space. Specifically, a log-linear model for LLMs is considered in which numerical data can be predicted from its context through a network with softmax in the output layer of LLMs (i.e., language model head in self-attention). For this model, it is demonstrated that, in order to achieve state-of-the-art performance in numerical domains, the hidden representations of the LLM embeddings must possess a structure that accounts for the shift-invariance of the softmax function. By formulating a gradient structure of self-attention in pre-trained models, it is shown how the isotropic property of LLM embeddings in contextual embedding space preserves the underlying structure of representations, thereby resolving the shift-invariance problem and providing a performance guarantee. Experiments show that different characteristics of numerical data and model architectures have different impacts on isotropy, and this variability directly affects the performances.